In this subsection, we evaluate the prediction performance of different rank determination methods. We adopt the same simulation settings in the main text to generate the training and test data sets. For each estimated coefficient matrix \(\hat{C}\) , we calculate the mean squared prediction error (MSPE) on the test data \(\lbrace \widetilde{X},\widetilde{Y}\rbrace \)  with a refitted estimator [1]}. The simulation results are summarized in Table REF . Our method still performs well with the smallest MSPE in most cases although the difference of the MSPE's is small. This is partially because that a slightly overestimated rank may not cause a significant increase of MSPE, while an underestimated rank often leads to a substantial increase of MSPE (see Section B.1.1).
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